Recent technologies enable matching intermediaries to engage in unprecedented levels of targeting, whereby matches finely depend on the agents' characteristics, but also favor customized (i.e., match-specific) pricing. Yet, novel regulations on the transfer of personal data, as well as a renewed trend towards market decentralization, are expected to hinder price customization and favor uniform pricing (whereby the price of a match charged to agents on a given side of a market is invariant in the agents' observable characteristics). To assess the impact of these developments, we build a matching model in which agents' preferences are both vertically and horizontally differentiated. Mirroring current practices, we show how, absent regulations, platforms maximize profits through price customization, link the latter to structural elasticities, and assess the targeting effects of market power. Perhaps surprisingly, we show that uniform pricing may either increase or decrease targeting levels and consumer welfare, depending on testable properties of demand. The analysis has implications for online shopping, ad-exchanges, and media platforms.